Control systems are described by equations (eg differential equations), but their properties of interest are most naturally expressed in terms of the system trajectories (the set of all solutions to the equations). This is formalized by the relatively new notion of the system behaviour, due to Willems. The manipulation of system equations on the other hand can be formalized using algebra, more precisely module theory for linear systems. The relationship between modules and behaviours is very rich and leads to deep results on system structure.
The aim of this project is to investigate this module-behaviour correspondence and apply it to deepen our understanding of control systems theory and address outstanding problems. We are particularly interested in the application area of multidimensional systems, i.e. systems described by partial differential equations or the discrete equivalent. In this area, we have to date had much success using these tools, eg in the characterization of controllability, the definition, characterization and decomposition of system poles, and the investigation of the relationship between feedback and trajectory control. Current areas of work include the extension to systems with variable coefficients, and the development of a general theory of model reduction and system identification for such systems.